Maximal transcendental weight contribution of scattering amplitudes

Abstract: Feynman integrals in quantum field theory evaluate to special functions and numbers that are usefully described by the notion of transcendental weight. In this paper, we propose a way of projecting a given dimensionally-regularised Feynman integral, for example contributing to a scattering amplitudes, onto its maximal weight part. The method uses insights into the singularity structure of space-time loop integrands, and is complementary to usual generalised unitarity approaches. We describe the method and give a proof-of-principle application to the two-loop scattering amplitudes $gg \to H$ in the heavy top-quark mass limit, which involves both planar and non-planar Feynman integrals. We also comment on further possible applications and discuss subtleties related to evanescent integrand terms.